A heritage building in central Christchurch will be demolished because the Ministry of Justice feels it is too expensive to save.

The Environment Court building, which has the highest heritage ranking, has been given a demolition order by the Canterbury Earthquake Recovery Authority (Cera).

The Armagh St building, formerly the Canterbury Society of Arts Gallery, has a distinctive brick facade and was completed in 1890.

The New Zealand Historic Places Trust (NZHPT) commissioned engineers to assess the building and recommended it be repaired as it was largely undamaged.

It said it would support retaining the brick facade, with a new building behind.

But a letter from the ministry says retaining the facade would be disruptive for the nearby Family Court and cost $2 million more than full demolition.

"Indications are that the cost of partial demolition, including remedial works and build, is significantly more expensive (approximately$2m) than full demolition and a new build, yet offers no additional service to the people of Christchurch," it says.

Cera operations general manager Warwick Isaacs said there was no choice but to demolish the building.

"It is a damaged and dangerous building at risk of collapse in a moderate earthquake," he said.

"We have a responsibility to deal with those buildings. Where the owners support retention, we let them do that. They give us a plan.

"When they are not prepared or able to do that, there is no choice for the owner than to have it demolished."

The building is owned by Ngai Tahu, with the ministry as the tenant.

Isaacs said Ngai Tahu supported the ministry's view on the repair costs.

Ngai Tahu Property chief executive Tony Sewell said it was working closely with the ministry.

"We are proud to have the ministry as our tenant and understand, like organisations throughout the city, that they have worked ceaselessly to carry out their services in challenging circumstances," he said.

The demolition order for the building has angered heritage advocates.

Iconic chairman Ian Lochhead said the demolition order was "mind-boggling".

"I think it is absolutely extraordinary that so little regard is being given to heritage buildings that are completely capable of being repaired," he said.

"I don't think the NZHPT would have been advising for the retention of those buildings if they had not been convinced that they could be retained at reasonable cost. There is no consideration being given to the larger picture here."